There is a progression: strength, then power, then speed. Each one is necessary to achieve the next.
Based on what you lift, it sounds as if you have the strength. It's not too hard to convert power to speed via track-specific workouts (which it sounds like you're doing), so, I'd say you need to focus on making power: if you sprint for 20 seconds you need to make as many watts in the last 5 seconds as in the first 5. Power is more important later in your sprint - that's where it really requires the power to continue accelerating.
There are a lot of ways to do this, in the gym via olympic lifting and plyos, and bike workouts. I'd say that the golden goose is rolling accelerations, targeting good 15+ second power and shutting down when you bog down.
But the thing with this sort of question is that there are a million tricks, tips, caveats, and pieces of context - it's where a good coach can really help you out.